I'm so sorry to read this, OP. You are in a dreadful position, NONE of it your fault and are in a very vulnerable position at the moment so I really hope you do listen to all of the advice here because it sounds like you don't have a lot of people to fall back on for immediate help right now.
PLEASE take some time out from him NOW. He needs to know that you recognise his pattern of behaviour as abusive and won't tolerate it. Is there anyone you can go and stay with for a few days? Or someone who could come and stay with you?
You absolutely 100% need to report this to the police. I know it's after the fact but you need to be in protection mode now for both you and your baby. If the incidents aren't recorded then you will have little to back up your side of any custody disputes moving forward.
Don't worry about him having marks on him, they are not from fighting, they are from you defending yourself. This also needs to be made clear to the Police.
Social Services will NOT be looking to remove your child from your care because you have suffered abuse BUT they will take it very, very seriously if you continue to live with this man, AND RIGHTLY SO! He is clearly not in control of himself when angry, he will 100% do it again and SS's position will be the protection of the child. The bottom line is, if he can put his hands on you in a temper, he can put his hands on your baby in a temper!! His apologies after the fact are worth nothing. He cannot change or make it up to you. It's been twice now, he was sober the first time and if you stay with him you are giving him the clear message that you WILL put up with his abuse and you WILL allow it to happen around your child.
NOTHING you SAY makes him putting his hands on you acceptable!! PLEASE take some time to accept that and get some help!
I'm so, so sorry you're going through this. This type of man prey on women who are isolated and damaged. Women who have been in care are more likely to suffer domestic abuse. You need to make a break for yourself. You deserve so much better.x.